Show commands:
SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 115920cm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.dq1 | 115920cm1 | \([0, 0, 0, -2427, -39254]\) | \(14295828483/2254000\) | \(249274368000\) | \([2]\) | \(110592\) | \(0.90963\) | \(\Gamma_0(N)\)-optimal |
| 115920.dq2 | 115920cm2 | \([0, 0, 0, 4293, -218006]\) | \(79119341757/231437500\) | \(-25595136000000\) | \([2]\) | \(221184\) | \(1.2562\) |
Rank
sage: E.rank()
The elliptic curves in class 115920cm have rank \(1\).
Complex multiplication
The elliptic curves in class 115920cm do not have complex multiplication.Modular form 115920.2.a.cm
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
